Reconstructive Integral GeometryAuthor: Victor Palamodov Published by Birkhäuser Basel ISBN: 978-3-0348-9629-0 DOI: 10.1007/978-3-0348-7941-5Table of Contents:Distributions and Fourier Transform Radon Transform The Funk Transform Reconstruction from Line Integrals Flat Integral Transform Incomplete Data Problems Spherical Transform and Inversion Algebraic Integral Transform Notes Topics: Mathematics, Fourier analysis, Integral transforms, Fourier analysis, Integral transforms,...
An Introduction to Basic Fourier SeriesAuthor: Sergei K. Suslov Published by Springer US ISBN: 978-1-4419-5244-8 DOI: 10.1007/978-1-4757-3731-8Table of Contents:Introduction Basic Exponential and Trigonometric Functions Addition Theorems Some Expansions and Integrals Introduction of Basic Fourier Series Investigation of Basic Fourier Series Completeness of Basic Trigonometric Systems Improved Asymptotics of Zeros Some Expansions in Basic Fourier Series Basic Bernoulli and Euler Polynomials and... Topics: Mathematics, Fourier analysis, Functions, Special, Fourier analysis, Functions, Special, Mathematics
byTrigub, Roald M., author; Belinsky, Eduard S., author
Fourier Analysis and Approximation of FunctionsAuthor: Roald M. Trigub, Eduard S. Bellinsky Published by Springer Netherlands ISBN: 978-90-481-6641-1 DOI: 10.1007/978-1-4020-2876-2Table of Contents:Representation Theorems Fourier Series Fourier Integral Discretization. Direct and Inverse Theorems of Approximation Theory Extremal Problems of Approximation Theory Representability of a Function as the Fourier Transform of a Measure Fourier Multipliers Methods of Summability of Fourier Series.... Topics: Fourier analysis, Approximation theory, Functions, Approximation theory, Fourier analysis, Functions
Examples and Theorems in AnalysisAuthor: Peter Leslie Walker BA, PhD Published by Springer London ISBN: 978-1-85233-493-2 DOI: 10.1007/978-0-85729-380-0Table of Contents:Sequences Functions and Continuity Differentiation Constructive Integration Improper Integrals Series Applications Topics: Mathematical analysis, Calculus, Fourier analysis
byBall, Joseph A; Helton, J. William; Klaus, Martin; Rodman, L
Current Trends in Operator Theory and its ApplicationsAuthor: Joseph A. Ball, J. William Helton, Martin Klaus, Leiba Rodman Published by Birkhäuser Basel ISBN: 978-3-0348-9608-5 DOI: 10.1007/978-3-0348-7881-4Table of Contents:Inverse Scattering Transform, KdV, and Solitons The Schur Algorithm for Generalized Schur Functions IV: Unitary Realizations Linear Systems with Schrödinger Operators and Their Transfer Functions Strongly Regular J-Inner Matrix Functions and Related Problems Boundary... Topics: Mathematics, Fourier analysis, Operator theory, Systems theory
byBrandolini, Luca; Colzani, Leonardo; Travaglini, Giancarlo; Iosevich, Alex
Fourier Analysis and ConvexityAuthor: Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini, Alex Iosevich Published by Birkhäuser Boston ISBN: 978-1-4612-6474-3 DOI: 10.1007/978-0-8176-8172-2Table of Contents:Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis Totally Geodesic Radon Transform of L Fourier Techniques in the Theory of Irregularities of Point Distribution Spectral Structure of Sets of Integers 100 Years of Fourier Series and Spherical... Topics: Fourier analysis, Convex geometry, Discrete geometry, Convex geometry, Discrete geometry, Fourier...
Integral Geometry and Convolution EquationsAuthor: V. V. Volchkov Published by Springer Netherlands ISBN: 978-94-010-3999-4 DOI: 10.1007/978-94-010-0023-9Table of Contents:Sets and Mappings Some Classes of Functions Distributions Some Special Functions Some Results Related to Spherical Harmonics Fourier Transform and Related Questions Partial Differential Equations Radon Transform Over Hyperplanes Comments and Open Problems Functions with Zero Averages Over Balls on Subsets of the Space ℝ... Topics: Mathematics, Fourier analysis, Integral equations, Differential equations, Partial, Differential...
Transforms and Fast Algorithms for Signal Analysis and RepresentationsAuthor: Guoan Bi, Yonghong Zeng Published by Birkhäuser Boston ISBN: 978-1-4612-6499-6 DOI: 10.1007/978-0-8176-8220-0Table of Contents:Introduction Polynomial Transforms and Their Fast Algorithms Fast Fourier Transform Algorithms Fast Algorithms for 1D Discrete Hartley Transform Fast Algorithms for MD Discrete Hartley Transform Fast Algorithms for 1D Discrete Cosine Transform Fast Algorithms for MD Discrete Cosine Transform... Topics: Mathematics, Computer software, Fourier analysis, Algorithms, Computer engineering, Algorithms,...
Theorem. Riesz Representation Theorem If H is a hilbert space and g : H_C (a functional) is linear and continuous then _y _ H such that g(x) = , _x _ H� Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1495
Density of the Schwartz Functions: To prove this we need to show the existence of a sequence of functions fn _ Sn for each f _ L2(R) such that fn f. Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1479
De�nition. A Banach Space is a complete normed space. i.e. every Cauchy sequence in L1(X, �) is convergent. Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1480
Now say that X is a set, R is a ring of subsets and we have a function � : R _ [0, �). This is the �measure�, what we�re looking for. One of the properties we need for this function is additivity : �(A _ B) = �(A) + �(B), if A, B _ R, A _ B = _ From just this property we can derive a number of properties about �.... Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1498
Poisson Summation: This is really a correlation between fourier transforms and fourier series Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1499
Start with simple functions, f : X [-� , �] is simple if it takes only �nitely many values. Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1487
to �nish our proof we must show that �_ is a countably additive measure Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics Source: http://www.flooved.com/reader/1500
Tauberian Theory: A Century of DevelopmentsAuthor: Jacob Korevaar Published by Springer Berlin Heidelberg ISBN: 978-3-642-05919-3 DOI: 10.1007/978-3-662-10225-1Table of Contents:The Hardy—Littlewood Theorems Wiener’s Theory Complex Tauberian Theorems Karamata’s Heritage: Regular Variation Extensions of the Classical Theory Borel Summability and General Circle Methods Tauberian Remainder Theory Topics: Mathematics, Fourier analysis, Integral transforms, Sequences (Mathematics), Number theory, Fourier...
A Handbook of Real Variables: With Applications to Differential Equations and Fourier AnalysisAuthor: Steven G. Krantz Published by Birkhäuser Boston ISBN: 978-1-4612-6409-5 DOI: 10.1007/978-0-8176-8128-9Table of Contents:Basics Sequences Series The Topology of the Real Line Limits and the Continuity of Functions The Derivative The Integral Sequences and Series of Functions Some Special Functions Advanced Topics Differential Equations Topics: Functions of real variables, Mathematical analysis, Linearer Operator, Kernfunktion, Reelle...
Multiscale Potential Theory: With Applications to GeoscienceAuthor: Willi Freeden, Volker Michel Published by Birkhäuser Boston ISBN: 978-1-4612-7395-0 DOI: 10.1007/978-1-4612-2048-0Table of Contents:Introduction Preliminary Tools Boundary-Value Problems of Potential Theory Boundary-Value Problems of Elasticity Satellite Problems The Gravimetry Problem Conclusion Hints for the Solution of the Exercises Topics: Mathematics, Geography, Physical geography, Fourier analysis, Potential theory (Mathematics),...
The successful operation of unmanned air vehicles requires software with a high degree of autonomy. Only if high level functions can be carried out without human control and intervention, complex missions in a changing and potentially unknown environment can be carried out successfully. Autonomy software is highly mission and safety critical: failures, caused by flaws in the software cannot only jeopardize the mission, but could also endanger human life (e.g., a crash of an UAV in a densely... Topics: BLACK HOLES (ASTRONOMY), VARIABILITY, ENERGY SPECTRA, COMPTON EFFECT, POWER SPECTRA, FOURIER...
We will be discussing �compact operators� later, so we need some sort of idea of com_pactness. This is what the following theorem provides. Topics: Maths, Topology and Metric Spaces, Differential Equations (ODEs & PDEs), Compact Spaces,... Source: http://www.flooved.com/reader/1481
Fourier series allow you to expand a function on a �nite interval as an in�nite series of trigonometric functions. What if the interval is in�nite? That�s the subject of this chapter. Instead of a sum over frequencies, you will have an integral. Topics: Physics, Mathematical Methods in Physics, Calculus and Analysis, Fourier Analysis, Physics Source: http://www.flooved.com/reader/2862
byMarkatos, N. C.; Spalding, D. B.; Tatchell, D. G
The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are... Topics: INDUCTION MOTORS, INVERTERS, WAVEFORMS, FOURIER ANALYSIS, PERFORMANCE TESTS, SPACECRAFT POWER...
We propose a new approach to performing ultrafast beam switching using two coupled Vertical-Cavity Surface-Emitting Lasers (VCSELs). The strategy is demonstrated by numerical simulation, showing a beam switching of 10 deg at 42 GHz. Topics: EIGENVALUES, GALERKIN METHOD, DISCRETIZATION (MATHEMATICS), OPERATORS (MATHEMATICS), DIFFUSION,...
Real-time Fourier analysis is provided by "bucket brigade' charge-transfer shift register. Device is small, inexpensive integrated circuit which does analog-to-digital-to-analog conversion, data processing, and time delay. Topics: NASA Technical Reports Server (NTRS), FOURIER ANALYSIS, SHIFT REGISTERS, SIGNAL ANALYSIS,...
Fourier series started life as a method to solve problems about the �ow of heat through ordinary materials. It has grown so far that if you search our library�s catalog for the keyword �Fourier� you will �nd 618 entries as of this date. It is a tool in abstract analysis and electromagnetism and statistics and radio communication and . . . . People have even tried to use it to analyze the stock market. (Itdidn�t help.) The representation of musical sounds as sums of waves of various... Topics: Physics, Mathematical Methods in Physics, Calculus and Analysis, Fourier Analysis, Physics Source: http://www.flooved.com/reader/2863
byJones, William B. (William Branham), 1931-; Gallet, Roger M.
This atlas is devoted to the study of amplitude and phase from the diurnal analysis of foF2 monthly median.It is concerned with their variations - both systematic and random - as functions of latitude, season and solar activity. * The atlas contains a ser Topics: Fourier analysis--Ionosphere., Ionospheric radio wave propagation., Scattering amplitude (Nuclear...
THE SPACELAB PROGRAM IS DISCUSSED. TOPICS INCLUDE: PROJECT CONCEPTUALIZATION, GENERAL ORGANIZATION, SPACELAB USERS, SHUTTLE INTERFACES, CREW, MODELS, AND CONFIGURATIONS. DECISIONS WHICH MUST BE MADE IN THESE AREAS BY EUROPEAN GOVERNMENTS ARE ALSO DISCUSSED. Topics: ASTROPHYSICS, SHOCK FRONTS, SHOCK WAVE PROPAGATION, ENERGY DISSIPATION, FOURIER ANALYSIS,...
A class of conservative difference approximations for the steady full potential equation was presented. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. Rigorous proof indicated that these new schemes satisfied a new discrete entropy inequality, which ruled out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in the analysis is the construction of a new entropy inequality for the full... Topics: COMPRESSIBLE FLOW, EULER EQUATIONS OF MOTION, FOURIER ANALYSIS, FINITE DIFFERENCE THEORY, FINITE...
byLesyna, L.; Roellig, T.; Savage, M.; Werner, Michael W
For sensitive detection of astronomical continuum radiation in the 200 micron to 3 mm wavelength range, bolometers are presently the detectors of choice. In order to approach the limits imposed by photon noise in a cryogenically cooled telescope in space, bolometers must be operated at temperatures near 0.1 K. Researchers report progress in building and using bolometers that operate at these temperatures. The most sensitive bolometer had an estimated noise equivalent power (NEP) of 7 x 10(exp... Topics: APERTURES, FOURIER ANALYSIS, MICROWAVE ANTENNAS, MILLIMETER WAVES, NEAR FIELDS, ACCURACY, COST...
A six degree-of-freedom computer-controlled manipulator is examined, and the relationships between the arm's joint variables and 3-space are derived. Arm trajectories using sequences of third-degree polynomials to describe the time history of each joint variable are presented and two approaches to the avoidance of obstacles are given. The equations of motion for the arm are derived and then decomposed into time-dependent factors and time-independent coefficients. Several new and simplifying... Topics: COMPUTER PROGRAMS, HARMONIC ANALYSIS, SIGNAL TO NOISE RATIOS, APPROXIMATION, AUTOCORRELATION,...
Methods of Applied Mathematics with a MATLAB OverviewAuthor: Jon H. Davis Published by Birkhäuser Boston ISBN: 978-1-4612-6486-6 DOI: 10.1007/978-0-8176-8198-2Table of Contents:Introduction Fourier Series Elementary Boundary Value Problems Sturm-Liouville Theory and Boundary Value Problems Functions of a Complex Variable Laplace Transforms Fourier Transforms Discrete Variable Transforms Additional Topics Linear Algebra Overview Software Resources Transform Tables Topics: MATLAB, Mathematics, Harmonic analysis, Fourier analysis, Functions of complex variables,...
The generation of surface waves on an infinite cylindrical antenna by a point source is examined, and the amplitude of the leaky-wave or the Goubau-wave, depending on the reactive surface loading, is determined. A Fourier-time analysis then gives the surface-wave transient, and in both cases it is found to take the form of a precursor outside the light cone. It is concluded that both these surface waves are non-causal in character, and that this property is likely to be a general one for... Topics: DTIC Archive, Lewin, Leonard, COLORADO UNIV AT BOULDER ELECTROMAGNETICS LAB, *SURFACE WAVES,...